Group Theoretical Methods In Image Understanding

Image understanding is an attempt to extract knowledge about a 3D scene from 20 images. The recent development of computers has made it possible to automate a wide range of systems and operations, not only in the industry, military, and special environments (space, sea, atomic plants, etc.), but also in daily life. As we now try to build ever more intelligent systems, the need for "visual" control has been strongly recognized, and the interest in image under standing has grown rapidly. Already, there exists a vast body of literature-ranging from general philosophical discourses to processing techniques. Compared with other works, however, this book may be unique in that its central focus is on "mathematical" principles-Lie groups and group representation theory, in particular. In the study of the relationship between the 3D scene and the 20 image, "geometry" naturally plays a central role. Today, so many branches are inter woven in geometry that we cannot truly regard it as a single subject. Neverthe less, as Felix Klein declared in his Erlangen Program, the central principle of geometry is group theory, because geometrical concepts are abstractions of properties that are "invariant" with respect to some group of transformations. In this text, we specifically focus on two groups of transformations. One is 20 rotations of the image coordinate system around the image origin. Such coordi nate rotations are indeed irrelevant when we look for intrinsic image properties.

Image understanding is an attempt to extract knowledge about a 3D scene from 20 images. The recent development of computers has made it possible to automate a wide range of systems and operations, not only in the industry, military, and special environments (space, sea, atomic plants, etc.), but also in daily life. As we now try to build ever more intelligent systems, the need for "visual" control has been strongly recognized, and the interest in image under standing has grown rapidly. Already, there exists a vast body of literature-ranging from general philosophical discourses to processing techniques. Compared with other works, however, this book may be unique in that its central focus is on "mathematical" principles-Lie groups and group representation theory, in particular. In the study of the relationship between the 3D scene and the 20 image, "geometry" naturally plays a central role. Today, so many branches are inter woven in geometry that we cannot truly regard it as a single subject. Neverthe less, as Felix Klein declared in his Erlangen Program, the central principle of geometry is group theory, because geometrical concepts are abstractions of properties that are "invariant" with respect to some group of transformations. In this text, we specifically focus on two groups of transformations. One is 20 rotations of the image coordinate system around the image origin. Such coordi nate rotations are indeed irrelevant when we look for intrinsic image properties.

In this volume the author gives an introduction to the theory of group representations and their applications in image science. The main feature of the presentation is a systematic treatment of the invariance principle in image processing and pattern recognition with the help of group theoretical methods. The invariance properties of a problem often largely define the solution to the problem. Invariance principles are well known in theoretical physics but their use in image processing is only a few years old. The reader will find that group theory provides a unifying framework for many problems in image science. The volume is based on graduate-level lectures given by the author, and the book is intended for students and researchers interested in theoretical aspects of computer vision.

This book contains 31 papers carefully selected from among those presented at the 7th Scandinavian Conference on Image Analysis. The authors have extended their papers to give a more in-depth discussion of the theory, or of the experimental validation of the method they have proposed. The topics covered are current and wide-ranging and include both 2D- and 3D-vision, and low to high level vision. Contents:Theory:Human Image Understanding (I Biederman)Local Image Structure (J J Koenderink)An Algebraic/Analytic Method for Reconstruction from Image Correspondences (G Sparr)Computational Aspects:Efficient Matching of Dynamically Changing Graphs (H Bunke et al.)Using a Genetic Algorithm to Solve Constraint Satisfaction Problems Generated by An Image Interpreter (S Truvé)Estimation of Velocity and Acceleration in Time Sequences (L Haglund et al.)Applications:Towards Continuously Operating Integrated Vision Systems for Robotics Applications (J L Crowley)Real Time 3D-Road Modeling for Autonomous Vehicle Guidance (U Franke)Studies on Classification of LANDSAT Image Data Using a Neural Network Approach (S Kamata et al.)Texture Discrimination of Normal and Malignant Mouse Liver Cell Nuclei (F Albregtsen et al.)and other papers Readership: Computer scientists and engineers. keywords:Image Analysis;Human Image Perception;T-junction;Feature;Extraction;Image Reconstruction;Autonomous Vehicle Guidance;3D Pose;Shape Analysis;Texture Analysis;Segmentation

This book contains 31 selected papers (out of 136 accepted) from the 9th Scandinavian Conference on Image Analysis, held in Uppsala, Sweden, 6-9 June 1995. They represent the very best of what is currently done in image analysis, world-wide, describing very recent work. The papers have been both considerably expanded and updated compared to the version in the conference proceedings, giving the readers a much better understanding of the issues at hand.The papers cover both theory and successful applications. There are chapters on Edges and Curves, Texture, Depth and Stereo, Scene Analysis, and 3D Motion, thus covering the chain from feature extraction to computer vision. Two important application areas are covered: Medical and Industrial.

Automatic image analysis has become an important tool in many fields of biology, medicine, and other sciences. Since the first edition of Image Analysis: Methods and Applications, the development of both software and hardware technology has undergone quantum leaps. For example, specific mathematical filters have been developed for quality enhancement of original images and for extraction of specific features of interest. Also, more complex programs have been developed for the analysis of object forms in distinguishing cancer cells from normal tissue cells. Just as significant, three-dimensional analysis of proteins, organelles, or macroscopic objects is even more complex. In addition, recent space-based experiments have optimized techniques for the extraction of movement parameters of numerous motile objects. The second edition of Image Analysis: Methods and Applications addresses all these new developments. Moreover, two new chapters have been added. One focuses on images on the internet, and the other discusses microscope image restoration. These chapters add significantly to the existing body of information on Internet communication protocol and environment as well as to that on image file formats considerations. The materials also include a list of internet Web sites that pertain to digital images and software along with those that relate to image processing. With these considerations in mind, Image Analysis: Methods and Application, Second Edition is of incalculable value to professionals, academics, and users of all aspects of image analysis in biology and other areas of science.

Ideal for classroom use and self-study, this book explains the implementation of the most effective modern methods in image analysis, covering segmentation, registration and visualisation, and focusing on the key theories, algorithms and applications that have emerged from recent progress in computer vision, imaging and computational biomedical science. Structured around five core building blocks - signals, systems, image formation and modality; stochastic models; computational geometry; level set methods; and tools and CAD models - it provides a solid overview of the field. Mathematical and statistical topics are presented in a straightforward manner, enabling the reader to gain a deep understanding of the subject without becoming entangled in mathematical complexities. Theory is connected to practical examples in x-ray, ultrasound, nuclear medicine, MRI and CT imaging, removing the abstract nature of the models and assisting reader understanding.